Properties and Graphical Representations of the 2-Variable Form of the Simsek Polynomials

Abstract

This article is written with an objective to introduce the 2-variable Simsek polynomials Yn(x,y;λ,δ) and to investigate some properties of these polynomials. The 2-variable forms of Changhee and Daehee polynomials are also considered. Several important recurrence relations involving the Cauchy, Changhee, Daehee and Simsek numbers are derived. The hypergeometric function representation for an integral involving these polynomials is obtained. The graphical representations of the 2-variable Simsek polynomials are considered for suitable values of the index n and parameters λ and δ. The article is concluded with the derivation of non-linear differential equation and related identity for the Simsek numbers.